Unitary divisor
= Unitary divisor
A <divisor> $d$ of a <positive integer> $n$ is unitary when $\gcd(d,n/d)=1$. Each <prime power> in the <prime factorization> of $n$ must therefore be included in $d$ completely or omitted completely. Consequently, the sum of the $k$-th powers of unitary divisors is $\prod_{p^e\parallel n}(1+p^{ek})$.